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okhsl.js
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okhsl.js
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import { toLinear } from "./linear.js";
import { fromOklab } from "./oklab.js";
import {
linearToOklab,
toe,
toeInv,
findCusp,
getStMax,
setAlpha,
TAU,
} from "./utils.js";
/**
* @typedef {number[]} okhsl
*
* All components in the range 0 <= x <= 1
* @see {@link https://bottosson.github.io/posts/colorpicker/#hsl-2}
*/
const findGamutIntersection = (a, b, L1, C1, L0, cusp = null) => {
if (!cusp) cusp = findCusp(a, b);
let t;
if ((L1 - L0) * cusp[1] - (cusp[0] - L0) * C1 <= 0) {
t = (cusp[1] * L0) / (C1 * cusp[0] + cusp[1] * (L0 - L1));
} else {
t = (cusp[1] * (L0 - 1)) / (C1 * (cusp[0] - 1) + cusp[1] * (L0 - L1));
const dL = L1 - L0;
const dC = C1;
const kl = 0.3963377774 * a + 0.2158037573 * b;
const km = -0.1055613458 * a - 0.0638541728 * b;
const ks = -0.0894841775 * a - 1.291485548 * b;
const l_dt = dL + dC * kl;
const m_dt = dL + dC * km;
const s_dt = dL + dC * ks;
const L = L0 * (1 - t) + t * L1;
const C = t * C1;
const l_ = L + C * kl;
const m_ = L + C * km;
const s_ = L + C * ks;
const l = l_ * l_ * l_;
const m = m_ * m_ * m_;
const s = s_ * s_ * s_;
const ldt = 3 * l_dt * l_ * l_;
const mdt = 3 * m_dt * m_ * m_;
const sdt = 3 * s_dt * s_ * s_;
const ldt2 = 6 * l_dt * l_dt * l_;
const mdt2 = 6 * m_dt * m_dt * m_;
const sdt2 = 6 * s_dt * s_dt * s_;
const r = 4.0767416621 * l - 3.3077115913 * m + 0.2309699292 * s - 1;
const r1 = 4.0767416621 * ldt - 3.3077115913 * mdt + 0.2309699292 * sdt;
const r2 = 4.0767416621 * ldt2 - 3.3077115913 * mdt2 + 0.2309699292 * sdt2;
const ur = r1 / (r1 * r1 - 0.5 * r * r2);
let tr = -r * ur;
const g = -1.2684380046 * l + 2.6097574011 * m - 0.3413193965 * s - 1;
const g1 = -1.2684380046 * ldt + 2.6097574011 * mdt - 0.3413193965 * sdt;
const g2 = -1.2684380046 * ldt2 + 2.6097574011 * mdt2 - 0.3413193965 * sdt2;
const ug = g1 / (g1 * g1 - 0.5 * g * g2);
let tg = -g * ug;
const b0 = -0.0041960863 * l - 0.7034186147 * m + 1.707614701 * s - 1;
const b1 = -0.0041960863 * ldt - 0.7034186147 * mdt + 1.707614701 * sdt;
const b2 = -0.0041960863 * ldt2 - 0.7034186147 * mdt2 + 1.707614701 * sdt2;
const ub = b1 / (b1 * b1 - 0.5 * b0 * b2);
let tb = -b0 * ub;
tr = ur >= 0 ? tr : 10e5;
tg = ug >= 0 ? tg : 10e5;
tb = ub >= 0 ? tb : 10e5;
t += Math.min(tr, tg, tb);
}
return t;
};
const getCs = (L, a_, b_) => {
const cusp = findCusp(a_, b_);
const Cmax = findGamutIntersection(a_, b_, L, 1, L, cusp);
const STmax = getStMax(a_, b_, cusp);
// prettier-ignore
const Smid = 0.11516993 + 1 / (
7.44778970 + 4.15901240 * b_
+ a_ * (- 2.19557347 + 1.75198401 * b_
+ a_ * (- 2.13704948 -10.02301043 * b_
+ a_ * (- 4.24894561 + 5.38770819 * b_ + 4.69891013 * a_
)))
);
// prettier-ignore
const Tmid = 0.11239642 + 1 / (
1.61320320 - 0.68124379 * b_
+ a_ * (+ 0.40370612 + 0.90148123 * b_
+ a_ * (- 0.27087943 + 0.61223990 * b_
+ a_ * (+ 0.00299215 - 0.45399568 * b_ - 0.14661872 * a_
)))
);
const k = Cmax / Math.min(L * STmax[0], (1 - L) * STmax[1]);
let Ca = L * Smid;
let Cb = (1 - L) * Tmid;
const Cmid =
0.9 *
k *
Math.sqrt(
Math.sqrt(1 / (1 / (Ca * Ca * Ca * Ca) + 1 / (Cb * Cb * Cb * Cb))),
);
Ca = L * 0.4;
Cb = (1 - L) * 0.8;
return [Math.sqrt(1 / (1 / (Ca * Ca) + 1 / (Cb * Cb))), Cmid, Cmax];
};
/**
* Updates a color based on Okhsl values and alpha.
* @alias module:pex-color.fromOkhsl
* @param {import("./color.js").color} color
* @param {number} h
* @param {number} s
* @param {number} l
* @param {number} [α]
* @returns {import("./color.js").color}
*/
export function fromOkhsl(color, h, s, l, α) {
if (l == 1) {
color[0] = color[1] = color[2] = 1;
} else if (l == 0) {
color[0] = color[1] = color[2] = 0;
} else {
const a_ = Math.cos(TAU * h);
const b_ = Math.sin(TAU * h);
let L = toeInv(l);
const [C0, Cmid, Cmax] = getCs(L, a_, b_);
let C, t, k0, k1, k2;
if (s < 0.8) {
t = 1.25 * s;
k0 = 0;
k1 = 0.8 * C0;
k2 = 1 - k1 / Cmid;
} else {
t = 5 * (s - 0.8);
k0 = Cmid;
k1 = (0.2 * Cmid * Cmid * 1.25 * 1.25) / C0;
k2 = 1 - k1 / (Cmax - Cmid);
}
C = k0 + (t * k1) / (1 - k2 * t);
return fromOklab(color, L, C * a_, C * b_, α);
}
return setAlpha(color, α);
}
/**
* Returns an Okhsl representation of a given color.
* @alias module:pex-color.toOkhsl
* @param {import("./color.js").color} color
* @param {Array} out
* @returns {okhsl}
*/
export function toOkhsl(color, out = []) {
toLinear(color, out);
linearToOklab(out[0], out[1], out[2], out);
const C = Math.sqrt(out[1] * out[1] + out[2] * out[2]);
const a_ = out[1] / C;
const b_ = out[2] / C;
const L = out[0];
out[0] = 0.5 + (0.5 * Math.atan2(-out[2], -out[1])) / Math.PI;
const [C0, Cmid, Cmax] = getCs(L, a_, b_);
out[2] = toe(L);
if (out[2] !== 0 && out[2] !== 1 && C !== 0) {
if (C < Cmid) {
const k0 = 0;
const k1 = 0.8 * C0;
const k2 = 1 - k1 / Cmid;
const t = (C - k0) / (k1 + k2 * (C - k0));
out[1] = t * 0.8;
} else {
const k0 = Cmid;
const k1 = (0.2 * Cmid * Cmid * 1.25 * 1.25) / C0;
const k2 = 1 - k1 / (Cmax - Cmid);
const t = (C - k0) / (k1 + k2 * (C - k0));
out[1] = 0.8 + 0.2 * t;
}
} else {
out[1] = 0;
}
// Epsilon for lightness should approach close to 32 bit lightness
// Epsilon for saturation just needs to be sufficiently close when denoting achromatic
let εL = 1e-7;
let εS = 1e-4;
const achromatic = Math.abs(out[1]) < εS;
if (achromatic || Math.abs(1 - out[2]) < εL) {
out[0] = 0; // null
if (!achromatic) out[1] = 0;
}
return out;
}